Estimating nearshore infragravity wave conditions at large spatial scales

Infragravity waves may contribute significantly to coastal flooding, especially during storm conditions. However, in many national and continental to global assessments of coastal flood risk, their contribution is not accounted for, mostly because of the high computational expense of traditional wave-resolving numerical models. In this study, we present an efficient stationary wave energy solver to estimate the evolution of incident and infragravity waves from offshore to the nearshore for large spatial scales. This solver can be subsequently used to provide nearshore wave boundary conditions for overland flood models. The new wave solver builds upon the stationary wave energy balance for incident wave energy and extends it to include the infragravity wave energy balance. To describe the energy transfer from incident to infragravity waves, an infragravity wave source term is introduced. This term acts as a sink term for incident waves and as a complementary source term for infragravity waves. The source term is simplified using a parameterized infragravity wave shoaling parameter. An empirical relation is derived using observed values of the shoaling parameter from a synthetic dataset of XBeach simulations, covering a wide range of wave conditions and beach profiles. The wave shoaling parameter is related to the local bed slope and relative wave height. As validation, we show for a range of cases from synthetic beach profiles to laboratory tests that infragravity wave transformation can be estimated using this wave solver with reasonable to good accuracy. Additionally, the validity in real-world conditions is verified successfully for DELILAH field case observations at Duck, NC, USA. We demonstrate the wave solver for a large-scale application of the full Outer Banks coastline in the US, covering 450 km of coastline, from deep water up to the coast. For this model, consisting of 4.5 million grid cells, the wave solver can estimate the stationary incident and infragravity wave field in a matter of seconds for the entire domain on a regular laptop PC. This computational efficiency cannot be provided by existing process-based wave-resolving models. Using the presented method, infragravity wave-driven flooding can be incorporated into large-scale coastal compound flood models and risk assessments

Multilevel multifidelity Monte Carlo methods for assessing uncertainty in coastal flooding

When choosing an appropriate hydrodynamic model, there is always a compromise between accuracy and computational cost, with high-fidelity models being more expensive than low-fidelity ones. However, when assessing uncertainty, we can use a multifidelity approach to take advantage of the accuracy of high-fidelity models and the computational efficiency of low-fidelity models. Here, we apply the multilevel multifidelity Monte Carlo method (MLMF) to quantify uncertainty by computing statistical estimators of key output variables with respect to uncertain input data, using the high-fidelity hydrodynamic model XBeach and the lower-fidelity coastal flooding model SFINCS (Super-Fast INundation of CoastS). The multilevel aspect opens up the further advantageous possibility of applying each of these models at multiple resolutions. This work represents the first application of MLMF in the coastal zone and one of its first applications in any field. For both idealised and real-world test cases, MLMF can significantly reduce computational cost for the same accuracy compared to both the standard Monte Carlo method and to a multilevel approach utilising only a single model (the multilevel Monte Carlo method). In particular, here we demonstrate using the case of Myrtle Beach, South Carolina, USA, that this improvement in computational efficiency allows for in-depth uncertainty analysis to be conducted in the case of real-world coastal environments – a task that would previously have been practically unfeasible. Moreover, for the first time, we show how an inverse transform sampling technique can be used to accurately estimate the cumulative distribution function (CDF) of variables from the MLMF outputs. MLMF-based estimates of the expectations and the CDFs of the variables of interest are of significant value to decision makers when assessing uncertainty in predictions